Learn Russian: Простому воину не одолеть этого тёмного колдуна. - A simple warrior cannot defeat this dark sorcerer.

In Russian, independent infinitive clauses don't have a standard nominative subject. Instead, the logical subject—the person experiencing the inevitability or impossibility—takes the dative case. Here, the simple warrior is the one for whom defeating the sorcerer is impossible.

How does не одолеть mean "cannot defeat" when there is no word for "can" in the sentence?

An independent infinitive combined with the negative particle не creates a strong, categorical sense of impossibility. It means the action simply cannot happen. You don't need a modal verb like не может because the grammatical structure itself implies that it is impossible for the dative subject to perform the action.

Why use the perfective verb одолеть instead of the imperfective одолевать in this negative construction?

When expressing impossibility with не plus an infinitive, you almost always use the perfective aspect to show that the successful result cannot be achieved. If you used the imperfective не одолевать, it would change the meaning to an instruction or an inevitability of not doing the action, translating closer to "should not defeat" or "is not supposed to defeat".

Is этого тёмного колдуна in the genitive case because of the negative не?